IDEAS home Printed from https://ideas.repec.org/p/sce/scecf5/252.html
   My bibliography  Save this paper

Trend and Cycles: A New Approach and Explanations of Some Old Puzzles

Author

Listed:
  • Tatsuma Wada
  • Pierre Perron

Abstract

Recent work on trend-cycle decompositions for US real GDP yields the following puzzling features: method based on Unobserved Components models, the Beveridge-Nelson decomposition, the Hodrick-Prescott filter and others yield very different cycles which bears little resemblance to the NBER chronology, ascribes much movements to the trend leaving little to the cycles, and some imply a negative correlation between the noise to the cycle and the trend. We argue that these features are artifacts created by the neglect of the presence of a change in the slope of the trend function in real GDP in 1973. Once this is properly accounted for, the results show all methods to yield the same cycle with a trend that is non-stochastic except for a few periods around 1973. This cycle is more important in magnitude than previously reported, it accords very well with the NBER chronology and imply no correlation between the trend and cycle, since the former is non-stochastic. We propose a new approach to univariate trend-cycle decompositions using a generalized Unobserved Components models with errors having a mixture of Normals distribution for both the slope of the trend function and the cycle components. It can account endogenously for infrequent changes such as level shifts and change in slope, as well as different variances for expansions and recessions. It yields a decomposition that accords very well with common notions of the business cycles

Suggested Citation

  • Tatsuma Wada & Pierre Perron, 2005. "Trend and Cycles: A New Approach and Explanations of Some Old Puzzles," Computing in Economics and Finance 2005 252, Society for Computational Economics.
  • Handle: RePEc:sce:scecf5:252
    as

    Download full text from publisher

    File URL: http://repec.org/sce2005/up.24513.1107144626.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
    2. Stock, James H & Watson, Mark W, 1988. "Variable Trends in Economic Time Series," Journal of Economic Perspectives, American Economic Association, vol. 2(3), pages 147-174, Summer.
    3. Beaudry, Paul & Koop, Gary, 1993. "Do recessions permanently change output?," Journal of Monetary Economics, Elsevier, vol. 31(2), pages 149-163, April.
    4. Sichel, Daniel E, 1993. "Business Cycle Asymmetry: A Deeper Look," Economic Inquiry, Western Economic Association International, vol. 31(2), pages 224-236, April.
    5. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
    6. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    7. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    8. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
    9. Saikkonen, Pentti & Luukkonen, Ritva, 1993. "Point Optimal Tests for Testing the Order of Differencing in ARIMA Models," Econometric Theory, Cambridge University Press, vol. 9(03), pages 343-362, June.
    10. John Y. Campbell & N. Gregory Mankiw, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 857-880.
    11. Sichel, Daniel E, 1994. "Inventories and the Three Phases of the Business Cycle," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 269-277, July.
    12. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    13. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    14. Stock, James H. & Watson, Mark W., 1999. "Business cycle fluctuations in us macroeconomic time series," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64 Elsevier.
    15. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    16. Charles Nelson & Eric Zivot, 2000. "Why are Beveridge-Nelson and Unobserved-Component Decompositions of GDP so Different?," Econometric Society World Congress 2000 Contributed Papers 0692, Econometric Society.
    17. Canova, Fabio, 1999. "Does Detrending Matter for the Determination of the Reference Cycle and the Selection of Turning Points?," Economic Journal, Royal Economic Society, vol. 109(452), pages 126-150, January.
    18. Morley, James C., 2002. "A state-space approach to calculating the Beveridge-Nelson decomposition," Economics Letters, Elsevier, vol. 75(1), pages 123-127, March.
    19. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    20. Sargan, J D & Bhargava, Alok, 1983. "Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors When the Root Lies on the Unit Circle," Econometrica, Econometric Society, vol. 51(3), pages 799-820, May.
    21. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    22. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    23. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 797-814.
    24. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    25. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
    26. Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-328, April.
    27. Ansley, Craig F. & Newbold, Paul, 1980. "Finite sample properties of estimators for autoregressive moving average models," Journal of Econometrics, Elsevier, vol. 13(2), pages 159-183, June.
    28. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Efectos no neutrales en los shocks monetarios
      by Nicolas Cachanosky in Punto de Vista Economico on 2013-11-15 09:01:59

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Testing for Shifts in Trend With an Integrated or Stationary Noise Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 369-396.
    2. Ghent, Andra, 2006. "Comparing Models of Macroeconomic Fluctuations: How Big Are the Differences?," MPRA Paper 180, University Library of Munich, Germany.
    3. Arabinda Basistha, 2009. "Hours per capita and productivity: evidence from correlated unobserved components models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 187-206.
    4. Arabinda Basistha, 2007. "Trend-cycle correlation, drift break and the estimation of trend and cycle in Canadian GDP," Canadian Journal of Economics, Canadian Economics Association, vol. 40(2), pages 584-606, May.
    5. B. Bhaskara Rao, 2010. "Deterministic and stochastic trends in the time series models: a guide for the applied economist," Applied Economics, Taylor & Francis Journals, vol. 42(17), pages 2193-2202.

    More about this item

    Keywords

    Trend-Cycle Decomposition; Structural Change; Non Gaussian Filtering; Unobserved Components Model; Beveridge-Nelson Decomposition;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sce:scecf5:252. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum). General contact details of provider: http://edirc.repec.org/data/sceeeea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.